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Encuentre Ia funcion de potencia para el campo vectorial:F(x,y) = (xy2 - x2 ) i+ (x2y+y2 )j...

Question

Encuentre Ia funcion de potencia para el campo vectorial:F(x,y) = (xy2 - x2 ) i+ (x2y+y2 )j

Encuentre Ia funcion de potencia para el campo vectorial: F(x,y) = (xy2 - x2 ) i+ (x2y+y2 )j



Answers

Sketch the vector fields the $x y$ -plane. $$\vec{F}(x, y)=2 x \vec{i}+x \vec{j}$$

In this problem of vector field we have to verify that the vector Phyllis conservative and we have given that Director field is F F x Y is equal to one divided with x squared. And they said why I minus X. City? So when we compare it, so M is equal to why divided with excess square and n is equal to minus X divided with extra square which is minus one divided with X. Now we have to find the differentiation of partial differentiation of and with respect to Y and partial differentiation of and with respect to X. No when we differentiated so differentiation of Y is simply one. So this is simply one divide with excess square and differentiation of minus one divided with access minus minus plus. So this is one divide with X square plus one divide with excess square. So now we say that partial differentiation of and with respect to Y is equal to partial differentiation of end with respect to X which is equal to one is divided with texas square. So we say that the function or we say that Director Field F is conservative is conservative. So we have the right answer as conservative

It is problem of vector field we have to verify that director feel is conservative and we have given the vector field F of X. Y is equal to 12 X. Y plus six, multiplied with x squared plus Y. J. So when we compare it, so this is M. And here this is the end. Now first we have to do is differentiation of the partial differentiation of em with respect to Y and partial differentiation of And with respect to X. Now differentiation of 12 X. Y. With respect to Y is simply 12 X differentiation of this term with respect to X as he simply this is 12 X. And why is it is constant? So this is zero. And now we see that differentiation of partial differentiation of em with respect to Y is equal to partial differentiation of and with respect to X is equals. So we say that this is the F is conservative. So we have the answer as this is conservative. So we have the right answer is conservative.

In this problem of vector field we have to determine if the vector field is conservative or not. So we have given the vector field F of X. Y is equal to one divided with under root of X squared plus Y squared multiplied with X. I plus O, Y J. Or this can be written as X divided with under root of X squared plus Y is square I plus why divided with under root of X squared plus Y squared multiplied with tea coefficient of I. Is called M. And co efficient of G is called And now we have to find the partial differentiation of em with respect to Y and partial differentiation of and with respect to X. Now here exist ticket as constant. So here X and differentiation of one divided with route and the route of X squared plus Y square is here. This will be will be minus half multiplied with this age one divided with X squared plus y squared to the power this age three divided with two and different vision of excess square is simply to X. And now similarly here we have to differentiate with respect to X. Here this way would be to white because we are doing the difference in with respect to Y. So this is two way and now here we are differentiating it with respect to X. So here why is stated is constant. So why? And different vision of this term is again minus one divided with two. And under one divide with this is X squared plus y squared to the power three develop to a different section of, say excess where is simply to X. Now when we see it, so this both are same so we can see that differentiation of and with respect to Y is equal to the differentiation of and with respect to X. So we say that director field F is conservative, so this is conservative vector field.

In this problem of vector field we have to determine if the vector field is conservative and we have given the vector field F F X Y is equal to two divided with Y is square, multiplied with E. To the power to X divided with Y. And multiplied with why I minus X. G. Or we can write it as say two divided with this is multiplied it twice. So this is to divide with Y and Z. To the power two weeks, divide with y minus, this is two X divided with Y is squared, multiplied with E. To the power to works, divide with white energy coefficient of is called M. And co efficient of G is called. And now we have to find the partial definition of and with respect to Y and partially transition of and with respect to X if both are same, we see that the funds obviously that the vector field F of x Y is conservative. So when we do the partial definition of this term with respect to Y. So this is equals two -2, multiplied with y plus two x divided with white cube and multiplied with E. To the power to X, divide with Y. And again when we do the differentiation of this time with respect to X. So we got the same ritual which is minus two, multiplied with Y plus two weeks divided with white cube and again multiplied with into the power two weeks divided with white. Now we say that the partial differentiation of em with respect to Y is equal to partial differentiation of and with respect to X. So that's why the vector field is conservative. So we have the right answer as director village conservative.


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